Turán Densities of Some Hypergraphs Related to $K_{k+1}^{k}$

Turán Densities of Some Hypergraphs Related to Kk+1k

Turán densities of some hypergraphs related to K k k + 1 ∗

Department of Mathematics, University of Illinois, 1409 W. Green Street Urbana, IL 61801, [email protected] Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, PA 15213, [email protected] Trinity College, Cambridge CB2 1TQ England, [email protected] Department of Mathematical Sciences, University of Memphis, Memphis, TN 38152, USA. 4 Department of Mathemat...

Turán Densities of Some Hypergraphs Related to K

Let B (k) i be the k-uniform hypergraph whose vertex set is of the form S ∪ T , where |S| = i, |T | = k− 1 and S ∩ T = ∅, and whose edges are the k-subsets of S ∪ T that contain either S or T . We derive upper and lower bounds for the Turán density of B (k) i that are close to each other as k → ∞. We also obtain asymptotically tight bounds for the Turán density of several other infinite familie...

Turán numbers for Berge - hypergraphs and related 1 extremal problems

4 Let F be a graph. We say that a hypergraph H is a Berge-F if there is a bijection 5 f : E(F )→ E(H) such that e ⊆ f(e) for every e ∈ E(F ). Note that Berge-F actually 6 denotes a class of hypergraphs. The maximum number of edges in an n-vertex r-graph 7 with no subhypergraph isomorphic to any Berge-F is denoted exr(n,Berge-F ). In this 8 paper we establish new upper and lower bounds on exr(n,...

On some number densities related to coprimes

1 S. Sykora, On some number densities related to coprimes, DOI: 10.3247/SL5Math14.005 On some number densities related to coprimes Stanislav Sykora, Extra Byte, www.ebyte.it First published in November 15, 2014 This brief essay explores the limit mean densities of subsets of natural numbers m such that the pair (m, m\b) is either coprime or not coprime. Here m\b = floor(m/b) denotes the operati...